A Blaschke-Santaló inequality for unconditional log-concave measures

The Blaschke-Santaló inequality states that the volume product $\mathrm{\mid }K\mathrm{\mid }\cdot \mathrm{\mid }{K}^o\mathrm{\mid }$ of a symmetric convex body $K\subset {\mathbb{R}}^n$ is maximized by the standard Euclidean unit-ball. Cordero-Erausquin asked whether the inequality remains true for all even log-concave measures. We briefly survey the literature around this question and provide details for the known fact that the inequality holds true for all unconditional log-concave measures.